Q: Find the domain of the function $$F(x) = \dfrac{\sqrt{2x + 6}}{x - 2}.$$

$$\{x \mid x \u003e -3, x \neq 2\}$$

Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each element in the domain is paired with exactly one element in the range.

Question 2

Given the set of ordered pairs $$\{(2, 5), (3, 7), (2, 8), (4, 9)\}$$, is this relation a function?

Accepted Answer

No, because the input 2 is paired with two different outputs.

Question 3

If $$f(x) = 2x^2$ - 5x + 3$$, what is $$f(3)$$?

Accepted Answer

$$f(3) = 3$$

Question 4

Which of the following equations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$x = y^2$

Question 5

A company charges a flat fee of $$\50$ plus $$\$$10$$ per hour for consulting. Which function models the total cost $$C as a $$function of hours $$h$$?

Accepted Answer

$$C(h) = 10h + 50$$

Question 6

Find the domain of the function $$F(x) = \dfrac{\sqrt{2x + 6}}{x - 2}.$$

Accepted Answer

$$\{x \mid x \u003e -3, x 
eq 2\}$$

Question 7

Given $$f(x) = x^2$ and g(x) = x + 1$, what is (f + g)(2$$)$$?

Accepted Answer

$$(f + g)(2) = 7$$

Question 8

If $$f(x) = \dfrac{1}{x}$$ and $$g(x) = x - 3$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$\{x \mid x 
eq 3\}$$

Question 9

The difference quotient for a function $$f is $$given by $$\dfrac{f(x+h) - f(x)}{h}. $$For $$f(x) = x^2$, what is the simplified difference quotient?

Accepted Answer

$$2x + h$$

Question 10

A cube has side length $$s. $$The volume $$V as a $$function of $$s is$$ $$V(s) = s^3$. What is the appropriate domain for this function in a real-world context?

Accepted Answer

$$\{s \mid s \u003e 0\}$$

Question 11

Given $$f(x) = \dfrac{1}{x}$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$(f + g)(x)$$?

Accepted Answer

$$\{x \mid x \u003e 0\}$$

Question 12

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$(f - g)(x)$$?

Accepted Answer

$$x^2 - x - 6$

Question 13

A medical researcher models the temperature $$T (in$$ $$^\circC) of a $$patient as a function of time $$t (in $$hours) after taking medication: $$T(t) = 37 - 0.5t. $$What is the temperature 4 hours after taking the medication?

Accepted Answer

$$T(4) = 35^\circC$$

Question 14

Which of the following is the correct explicit form for the function defined implicitly by $$y + 2x = 7$$?

Accepted Answer

$$y = 7 - 2x$$

Question 15

If $$f(x) = \sqrt{x - 1}$$, what is the domain of $$f$$?

Accepted Answer

$$\{x \mid x \geq 1\}$$

Question 16

Given $$f(x) = x^2$ and g(x) = 2x$, what is (f$$ \cdot g)(3)$$?

Accepted Answer

$$(f \cdot g)(3) = 54$$

Question 17

A chemical reaction's rate $$R (in $$mol/L/s) is modeled by $$R(c) = \dfrac{5}{c - 2}$$, where $$c is $$the concentration in mol/L. What is the domain of $$R$$?

Accepted Answer

$$\{c \mid c 
eq 2\}$$

Question 18

If $$f(x) = x^2$ and g(x) = x + 1$, what is the quotient $$\left(\dfrac{f}{g}\right)(x)$$?

Accepted Answer

$$\dfrac{x^2$}{x + 1}$$

Question 19

Which of the following real-world scenarios is best modeled by a function?

Accepted Answer

The height of a ball thrown upward as a function of time.

Functions and Their Graphs: Precalculus Study Notes (Section 1.1)

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